Bunty has candies and chewing gums in his sweet box in the ratio 7:13. After he eats 8 candies and 11 chewing gums, the ratio becomes 1:2. How many candies does he have now?

Introduction / Context:
This problem is a good example of how ratios can change when certain items are added or removed, and how to convert those conditions into equations. It involves two categories, candies and chewing gums, and describes their numbers before and after Bunty eats some of them. Such questions test the learner's ability to represent ratios algebraically and solve a simple linear equation.

Given Data / Assumptions:

Initial ratio of candies to chewing gums = 7 : 13.
Bunty eats 8 candies.
Bunty eats 11 chewing gums.
The new ratio of candies to chewing gums becomes 1 : 2.
We need the number of candies remaining after Bunty has eaten some.

Concept / Approach:
Let the initial numbers of candies and gums be 7x and 13x respectively. After Bunty eats some items, the new counts are adjusted accordingly. The new ratio is given as 1:2, so we equate the algebraic ratio of the new counts to 1:2. This produces a linear equation in x that we can solve. Once x is known, we find the actual counts and in particular the current number of candies.

Step-by-Step Solution:
Let initial candies = 7x and initial chewing gums = 13x. After eating, candies left = 7x - 8. After eating, chewing gums left = 13x - 11. Given that the new ratio of candies to chewing gums is 1 : 2. So (7x - 8) / (13x - 11) = 1 / 2. Cross multiply: 2 * (7x - 8) = 1 * (13x - 11). Simplify: 14x - 16 = 13x - 11. Therefore x = 5. Candies now = 7x - 8 = 7 * 5 - 8 = 35 - 8 = 27.

Verification / Alternative check:
With x = 5, initial numbers are 35 candies and 65 chewing gums. After Bunty eats, candies become 27 and chewing gums become 54. The new ratio 27:54 simplifies by dividing both terms by 27, which gives 1:2. This matches the ratio stated in the problem, confirming that our algebraic setup and solution are correct.

Why Other Options Are Wrong:
Option 65 represents the initial number of chewing gums, not the candies remaining after Bunty eats some of them.
Option 35 corresponds to the initial number of candies before any are eaten, not the final number requested.
Option 54 is the final number of chewing gums, not the number of candies, so it does not answer the question asked.

Common Pitfalls:
Sometimes students confuse initial and final quantities and directly set 7:13 equal to 1:2 without accounting for items eaten.
Another typical mistake is to subtract the ratio numbers 7 and 13 by 8 and 11 instead of reducing the actual counts 7x and 13x by those numbers.
Some learners forget to cross multiply correctly and make algebraic mistakes when solving the resulting equation.

Final Answer:
After eating some sweets, Bunty now has 27 candies remaining in his box.